Problem Theory

The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here is why, Why are we Turing complete? Being Turing complete also means that somehow our brain implements the function that a universal Turing machine implements. The point is that evolution achieved Turing completeness, and then the explanation should be evolutionary, but our explanation is mathematical. The trick is to introduce a mathematical theory of problems, under the basic assumption that solving more problems provides more survival opportunities. So we build a problem theory by fusing set and computing theories. Then we construct a series of resolvers, where each resolver is defined by its computing capacity, that exhibits the following property: all problems solved by a resolver are also solved by the next resolver in the series if certain condition is satisfied. The last of the conditions is to be Turing complete. This series defines a resolvers hierarchy that could be seen as a framework for the evolution of cognition. Then the answer to our question would be: to solve most problems. By the way, the problem theory defines adaptation, perception, and learning, and it shows that there are just three ways to resolve any problem: routine, trial, and analogy. And, most importantly, this theory demonstrates how problems can be used to found mathematics and computing on biology.Comment: 43 page

Proof of Church's Thesis

We prove that if our calculating capability is that of a universal Turing machine with a finite tape, then Church's thesis is true. This way we accomplish Post (1936) program.Comment: 6 page

Numerical resolution of an exact heat conduction model with a delay term

In this paper we analyze, from the numerical point of view, a dynamic thermoelastic problem. Here, the so-called exact heat conduction model with a delay term is used to obtain the heat evolution. Thus, the thermomechanical problem is written as a coupled system of partial differential equations, and its variational formulation leads to a system written in terms of the velocity and the temperature fields. An existence and uniqueness result is recalled. Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A priori error estimates are proved, from which the linear convergence of the algorithm could be derived under suitable additional regularity conditions. Finally, a two-dimensional numerical example is solved to show the accuracy of the approximation and the decay of the discrete energy.Peer ReviewedPostprint (published version

Fast and robust learning by reinforcement signals: explorations in the insect brain

We propose a model for pattern recognition in the insect brain. Departing from a well-known body of knowledge about the insect brain, we investigate which of the potentially present features may be useful to learn input patterns rapidly and in a stable manner. The plasticity underlying pattern recognition is situated in the insect mushroom bodies and requires an error signal to associate the stimulus with a proper response. As a proof of concept, we used our model insect brain to classify the well-known MNIST database of handwritten digits, a popular benchmark for classifiers. We show that the structural organization of the insect brain appears to be suitable for both fast learning of new stimuli and reasonable performance in stationary conditions. Furthermore, it is extremely robust to damage to the brain structures involved in sensory processing. Finally, we suggest that spatiotemporal dynamics can improve the level of confidence in a classification decision. The proposed approach allows testing the effect of hypothesized mechanisms rather than speculating on their benefit for system performance or confidence in its responses

Prospects for the Oil-importing Countries of the Caribbean

As a region the Caribbean countries are net exporters of hydrocarbons. However, all exports of natural gas and crude oil are concentrated in one country, Trinidad and Tobago. The rest of the region taken as a whole is net importer of hydrocarbons. The largest countries in the region are heavily dependent on imported crude oil and products as their main source of primary energy. The trend has intensified over recent years. Net-importing countries in the region have more than doubled their annual per capita consumption of oil over the last two decades. Trinidad and Tobago could supply the region’s hydrocarbon needs. However, very little effort has been made by the importing countries to substitute gas from Trinidad and Tobago for oil from other extra regional sources. There are a number of initiatives under way to reduce the region’s dependence on imported hydrocarbons: Eastern Caribbean Gas Pipeline (ECGP); Eastern Caribbean Geothermal Energy Project (Geo-Caraïbes); Caribbean Renewable Energy Development Programme (CREDP); Petrocaribe Energy Cooperation Agreement and Production of Biofuels. The IDB together with CARICOM and the Caribbean Development Bank are concentrating efforts in to promote the development of biofuels in the region, with specific programs in the Dominican Republic, Haiti, Jamaica, and Trinidad and Tobago. Furthermore, there individual country efforts to implement mid-term plans to increase their energy efficiency and diversify their Energy Matrices away from oil, among these countries it is worth highlighting: Jamaica, Guyana and Barbados. Finally, the IDB is sponsoring a number of technical studies with the objectives of developing renewable energy and increasing energy efficiency. Beyond these initiatives, an avenue that is worth exploring is enhancing regional integration, especially through small-scale trading of natural gas between Trinidad and Tobago and the rest of the Caribbean.

Using high-frequency data and time series models to improve yield management

We show the potential contribution of time series models (TSM) to the analysis of high frequency (less than monthly) time series of economic activity. The evolution of the series is induced by stable patterns of behavior of economic agents; but these patterns are so complex that simple smoothing techniques or subjective forecasting can not consider all underlying factors and TSM are needed if a full efficient analysis is to be carried out. The main ideas are illustrated with an apllication to Spanish daily electricity consumption